LMFDB - Embedded newform 775.2.f.a.743.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(557,775)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("775.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			743.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	775.743
Dual form			775.2.f.a.557.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 1.22474i) q^{2} +(-1.00000 + 1.00000i) q^{3} -1.00000i q^{4} -2.44949i q^{6} +(-2.44949 + 2.44949i) q^{7} +(-1.22474 - 1.22474i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.22474 + 1.22474i) q^{2} +(-1.00000 + 1.00000i) q^{3} -1.00000i q^{4} -2.44949i q^{6} +(-2.44949 + 2.44949i) q^{7} +(-1.22474 - 1.22474i) q^{8} +1.00000i q^{9} +4.89898i q^{11} +(1.00000 + 1.00000i) q^{12} +(-3.00000 + 3.00000i) q^{13} -6.00000i q^{14} +5.00000 q^{16} +(5.00000 + 5.00000i) q^{17} +(-1.22474 - 1.22474i) q^{18} -2.00000i q^{19} -4.89898i q^{21} +(-6.00000 - 6.00000i) q^{22} +(1.00000 - 1.00000i) q^{23} +2.44949 q^{24} -7.34847i q^{26} +(-4.00000 - 4.00000i) q^{27} +(2.44949 + 2.44949i) q^{28} -9.79796 q^{29} +(5.00000 + 2.44949i) q^{31} +(-3.67423 + 3.67423i) q^{32} +(-4.89898 - 4.89898i) q^{33} -12.2474 q^{34} +1.00000 q^{36} +(3.00000 + 3.00000i) q^{37} +(2.44949 + 2.44949i) q^{38} -6.00000i q^{39} -6.00000 q^{41} +(6.00000 + 6.00000i) q^{42} +(3.00000 - 3.00000i) q^{43} +4.89898 q^{44} +2.44949i q^{46} +(7.34847 - 7.34847i) q^{47} +(-5.00000 + 5.00000i) q^{48} -5.00000i q^{49} -10.0000 q^{51} +(3.00000 + 3.00000i) q^{52} +(1.00000 - 1.00000i) q^{53} +9.79796 q^{54} +6.00000 q^{56} +(2.00000 + 2.00000i) q^{57} +(12.0000 - 12.0000i) q^{58} -12.0000i q^{59} +4.89898i q^{61} +(-9.12372 + 3.12372i) q^{62} +(-2.44949 - 2.44949i) q^{63} +1.00000i q^{64} +12.0000 q^{66} +(2.44949 - 2.44949i) q^{67} +(5.00000 - 5.00000i) q^{68} +2.00000i q^{69} +6.00000 q^{71} +(1.22474 - 1.22474i) q^{72} +(-3.00000 + 3.00000i) q^{73} -7.34847 q^{74} -2.00000 q^{76} +(-12.0000 - 12.0000i) q^{77} +(7.34847 + 7.34847i) q^{78} +9.79796 q^{79} +5.00000 q^{81} +(7.34847 - 7.34847i) q^{82} +(-7.00000 + 7.00000i) q^{83} -4.89898 q^{84} +7.34847i q^{86} +(9.79796 - 9.79796i) q^{87} +(6.00000 - 6.00000i) q^{88} +9.79796 q^{89} -14.6969i q^{91} +(-1.00000 - 1.00000i) q^{92} +(-7.44949 + 2.55051i) q^{93} +18.0000i q^{94} -7.34847i q^{96} +(6.12372 + 6.12372i) q^{98} -4.89898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3}+O(q^{10}) $ 4 * q - 4 * q^3	$ 4 q - 4 q^{3} + 4 q^{12} - 12 q^{13} + 20 q^{16} + 20 q^{17} - 24 q^{22} + 4 q^{23} - 16 q^{27} + 20 q^{31} + 4 q^{36} + 12 q^{37} - 24 q^{41} + 24 q^{42} + 12 q^{43} - 20 q^{48} - 40 q^{51} + 12 q^{52} + 4 q^{53} + 24 q^{56} + 8 q^{57} + 48 q^{58} - 12 q^{62} + 48 q^{66} + 20 q^{68} + 24 q^{71} - 12 q^{73} - 8 q^{76} - 48 q^{77} + 20 q^{81} - 28 q^{83} + 24 q^{88} - 4 q^{92} - 20 q^{93}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^12 - 12 * q^13 + 20 * q^16 + 20 * q^17 - 24 * q^22 + 4 * q^23 - 16 * q^27 + 20 * q^31 + 4 * q^36 + 12 * q^37 - 24 * q^41 + 24 * q^42 + 12 * q^43 - 20 * q^48 - 40 * q^51 + 12 * q^52 + 4 * q^53 + 24 * q^56 + 8 * q^57 + 48 * q^58 - 12 * q^62 + 48 * q^66 + 20 * q^68 + 24 * q^71 - 12 * q^73 - 8 * q^76 - 48 * q^77 + 20 * q^81 - 28 * q^83 + 24 * q^88 - 4 * q^92 - 20 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.22474	+	1.22474i	−0.866025	+	0.866025i	−0.992030	−	0.126004i	$-0.959785\pi$
$2$	−1.22474	+	1.22474i	−0.866025	+	0.866025i	0.126004	+	0.992030i	$0.459785\pi$
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	0.356822	+	0.934172i	$0.383860\pi$
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	1.00000i
$7$	−2.44949	+	2.44949i	−0.925820	+	0.925820i	−0.997433	−	0.0716124i	$-0.977186\pi$
$7$	−2.44949	+	2.44949i	−0.925820	+	0.925820i	0.0716124	+	0.997433i	$0.477186\pi$
$8$	−1.22474	−	1.22474i	−0.433013	−	0.433013i
$9$			1.00000i			0.333333i
$10$		0			0
$11$			4.89898i			1.47710i	0.674200	+	0.738549i	$0.264489\pi$
$11$			4.89898i			1.47710i	−0.674200	+	0.738549i	$0.735511\pi$
$12$	1.00000	+	1.00000i	0.288675	+	0.288675i
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	−0.987797	−	0.155747i	$-0.950222\pi$
$13$	−3.00000	+	3.00000i	−0.832050	+	0.832050i	0.155747	+	0.987797i	$0.450222\pi$
$14$		−	6.00000i		−	1.60357i
$15$		0			0
$16$	5.00000			1.25000
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	5.00000	+	5.00000i	1.21268	+	1.21268i	0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.22474	−	1.22474i	−0.288675	−	0.288675i
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$		0			0
$21$		−	4.89898i		−	1.06904i
$22$	−6.00000	−	6.00000i	−1.27920	−	1.27920i
$23$	1.00000	−	1.00000i	0.208514	−	0.208514i	−0.595121	−	0.803636i	$-0.702896\pi$
$23$	1.00000	−	1.00000i	0.208514	−	0.208514i	0.803636	+	0.595121i	$0.202896\pi$
$24$	2.44949			0.500000
$25$		0			0
$26$		−	7.34847i		−	1.44115i
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$	2.44949	+	2.44949i	0.462910	+	0.462910i
$29$	−9.79796			−1.81944			−0.909718	−	0.415227i	$-0.863702\pi$
$29$	−9.79796			−1.81944			−0.909718	+	0.415227i	$0.863702\pi$
$30$		0			0
$31$	5.00000	+	2.44949i	0.898027	+	0.439941i
$31$	5.00000	+	2.44949i	0.898027	+	0.439941i
$32$	−3.67423	+	3.67423i	−0.649519	+	0.649519i
$33$	−4.89898	−	4.89898i	−0.852803	−	0.852803i
$34$	−12.2474			−2.10042
$35$		0			0
$36$	1.00000			0.166667
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	0.909312	−	0.416115i	$-0.136609\pi$
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	−0.416115	+	0.909312i	$0.636609\pi$
$38$	2.44949	+	2.44949i	0.397360	+	0.397360i
$39$		−	6.00000i		−	0.960769i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	6.00000	+	6.00000i	0.925820	+	0.925820i
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$	4.89898			0.738549
$45$		0			0
$46$			2.44949i			0.361158i
$47$	7.34847	−	7.34847i	1.07188	−	1.07188i	0.0746766	−	0.997208i	$-0.476208\pi$
$47$	7.34847	−	7.34847i	1.07188	−	1.07188i	0.997208	−	0.0746766i	$-0.0237924\pi$
$48$	−5.00000	+	5.00000i	−0.721688	+	0.721688i
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$	−10.0000			−1.40028
$52$	3.00000	+	3.00000i	0.416025	+	0.416025i
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$	9.79796			1.33333
$55$		0			0
$56$	6.00000			0.801784
$57$	2.00000	+	2.00000i	0.264906	+	0.264906i
$58$	12.0000	−	12.0000i	1.57568	−	1.57568i
$59$		−	12.0000i		−	1.56227i	−0.624364	−	0.781133i	$-0.714642\pi$
$59$		−	12.0000i		−	1.56227i	0.624364	−	0.781133i	$-0.285358\pi$
$60$		0			0
$61$			4.89898i			0.627250i	0.949547	+	0.313625i	$0.101543\pi$
$61$			4.89898i			0.627250i	−0.949547	+	0.313625i	$0.898457\pi$
$62$	−9.12372	+	3.12372i	−1.15871	+	0.396713i
$63$	−2.44949	−	2.44949i	−0.308607	−	0.308607i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	12.0000			1.47710
$67$	2.44949	−	2.44949i	0.299253	−	0.299253i	−0.541468	−	0.840721i	$-0.682131\pi$
$67$	2.44949	−	2.44949i	0.299253	−	0.299253i	0.840721	+	0.541468i	$0.182131\pi$
$68$	5.00000	−	5.00000i	0.606339	−	0.606339i
$69$			2.00000i			0.240772i
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	1.22474	−	1.22474i	0.144338	−	0.144338i
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	−0.860527	−	0.509404i	$-0.829866\pi$
$73$	−3.00000	+	3.00000i	−0.351123	+	0.351123i	0.509404	+	0.860527i	$0.329866\pi$
$74$	−7.34847			−0.854242
$75$		0			0
$76$	−2.00000			−0.229416
$77$	−12.0000	−	12.0000i	−1.36753	−	1.36753i
$78$	7.34847	+	7.34847i	0.832050	+	0.832050i
$79$	9.79796			1.10236			0.551178	−	0.834388i	$-0.314178\pi$
$79$	9.79796			1.10236			0.551178	+	0.834388i	$0.314178\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$	7.34847	−	7.34847i	0.811503	−	0.811503i
$83$	−7.00000	+	7.00000i	−0.768350	+	0.768350i	−0.977816	−	0.209466i	$-0.932827\pi$
$83$	−7.00000	+	7.00000i	−0.768350	+	0.768350i	0.209466	+	0.977816i	$0.432827\pi$
$84$	−4.89898			−0.534522
$85$		0			0
$86$			7.34847i			0.792406i
$87$	9.79796	−	9.79796i	1.05045	−	1.05045i
$88$	6.00000	−	6.00000i	0.639602	−	0.639602i
$89$	9.79796			1.03858			0.519291	−	0.854598i	$-0.326196\pi$
$89$	9.79796			1.03858			0.519291	+	0.854598i	$0.326196\pi$
$90$		0			0
$91$		−	14.6969i		−	1.54066i
$92$	−1.00000	−	1.00000i	−0.104257	−	0.104257i
$93$	−7.44949	+	2.55051i	−0.772476	+	0.264476i
$94$			18.0000i			1.85656i
$95$		0			0
$96$		−	7.34847i		−	0.750000i
$97$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$97$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$98$	6.12372	+	6.12372i	0.618590	+	0.618590i
$99$	−4.89898			−0.492366
$100$		0			0
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$	12.2474	−	12.2474i	1.21268	−	1.21268i
$103$	2.44949	+	2.44949i	0.241355	+	0.241355i	0.817411	−	0.576055i	$-0.195409\pi$
$103$	2.44949	+	2.44949i	0.241355	+	0.241355i	−0.576055	+	0.817411i	$0.695409\pi$
$104$	7.34847			0.720577
$105$		0			0
$106$			2.44949i			0.237915i
$107$	7.34847	−	7.34847i	0.710403	−	0.710403i	−0.256216	−	0.966620i	$-0.582476\pi$
$107$	7.34847	−	7.34847i	0.710403	−	0.710403i	0.966620	+	0.256216i	$0.0824759\pi$
$108$	−4.00000	+	4.00000i	−0.384900	+	0.384900i
$109$			16.0000i			1.53252i	0.642529	+	0.766261i	$0.277885\pi$
$109$			16.0000i			1.53252i	−0.642529	+	0.766261i	$0.722115\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$	−12.2474	+	12.2474i	−1.15728	+	1.15728i
$113$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$113$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$114$	−4.89898			−0.458831
$115$		0			0
$116$			9.79796i			0.909718i
$117$	−3.00000	−	3.00000i	−0.277350	−	0.277350i
$118$	14.6969	+	14.6969i	1.35296	+	1.35296i
$119$	−24.4949			−2.24544
$120$		0			0
$121$	−13.0000			−1.18182
$122$	−6.00000	−	6.00000i	−0.543214	−	0.543214i
$123$	6.00000	−	6.00000i	0.541002	−	0.541002i
$124$	2.44949	−	5.00000i	0.219971	−	0.449013i
$125$		0			0
$126$	6.00000			0.534522
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	0.827570	−	0.561363i	$-0.189723\pi$
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	−0.561363	+	0.827570i	$0.689723\pi$
$128$	−8.57321	−	8.57321i	−0.757772	−	0.757772i
$129$			6.00000i			0.528271i
$130$		0			0
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$	−4.89898	+	4.89898i	−0.426401	+	0.426401i
$133$	4.89898	+	4.89898i	0.424795	+	0.424795i
$134$			6.00000i			0.518321i
$135$		0			0
$136$		−	12.2474i		−	1.05021i
$137$	−5.00000	−	5.00000i	−0.427179	−	0.427179i	0.460487	−	0.887666i	$-0.347675\pi$
$137$	−5.00000	−	5.00000i	−0.427179	−	0.427179i	−0.887666	+	0.460487i	$0.847675\pi$
$138$	−2.44949	−	2.44949i	−0.208514	−	0.208514i
$139$	14.6969			1.24658			0.623289	−	0.781992i	$-0.285796\pi$
$139$	14.6969			1.24658			0.623289	+	0.781992i	$0.285796\pi$
$140$		0			0
$141$			14.6969i			1.23771i
$142$	−7.34847	+	7.34847i	−0.616670	+	0.616670i
$143$	−14.6969	−	14.6969i	−1.22902	−	1.22902i
$144$			5.00000i			0.416667i
$145$		0			0
$146$		−	7.34847i		−	0.608164i
$147$	5.00000	+	5.00000i	0.412393	+	0.412393i
$148$	3.00000	−	3.00000i	0.246598	−	0.246598i
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$		0			0
$151$			14.6969i			1.19602i	0.801489	+	0.598010i	$0.204042\pi$
$151$			14.6969i			1.19602i	−0.801489	+	0.598010i	$0.795958\pi$
$152$	−2.44949	+	2.44949i	−0.198680	+	0.198680i
$153$	−5.00000	+	5.00000i	−0.404226	+	0.404226i
$154$	29.3939			2.36863
$155$		0			0
$156$	−6.00000			−0.480384
$157$	−9.79796	+	9.79796i	−0.781962	+	0.781962i	−0.980162	−	0.198199i	$-0.936491\pi$
$157$	−9.79796	+	9.79796i	−0.781962	+	0.781962i	0.198199	+	0.980162i	$0.436491\pi$
$158$	−12.0000	+	12.0000i	−0.954669	+	0.954669i
$159$			2.00000i			0.158610i
$160$		0			0
$161$			4.89898i			0.386094i
$162$	−6.12372	+	6.12372i	−0.481125	+	0.481125i
$163$	12.2474	+	12.2474i	0.959294	+	0.959294i	0.999203	−	0.0399091i	$-0.0127068\pi$
$163$	12.2474	+	12.2474i	0.959294	+	0.959294i	−0.0399091	+	0.999203i	$0.512707\pi$
$164$			6.00000i			0.468521i
$165$		0			0
$166$		−	17.1464i		−	1.33082i
$167$	7.00000	+	7.00000i	0.541676	+	0.541676i	0.924020	−	0.382344i	$-0.124883\pi$
$167$	7.00000	+	7.00000i	0.541676	+	0.541676i	−0.382344	+	0.924020i	$0.624883\pi$
$168$	−6.00000	+	6.00000i	−0.462910	+	0.462910i
$169$		−	5.00000i		−	0.384615i
$170$		0			0
$171$	2.00000			0.152944
$172$	−3.00000	−	3.00000i	−0.228748	−	0.228748i
$173$	−4.89898	−	4.89898i	−0.372463	−	0.372463i	0.495911	−	0.868373i	$-0.334834\pi$
$173$	−4.89898	−	4.89898i	−0.372463	−	0.372463i	−0.868373	+	0.495911i	$0.834834\pi$
$174$			24.0000i			1.81944i
$175$		0			0
$176$			24.4949i			1.84637i
$177$	12.0000	+	12.0000i	0.901975	+	0.901975i
$178$	−12.0000	+	12.0000i	−0.899438	+	0.899438i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$			9.79796i			0.728277i	0.931345	+	0.364138i	$0.118636\pi$
$181$			9.79796i			0.728277i	−0.931345	+	0.364138i	$0.881364\pi$
$182$	18.0000	+	18.0000i	1.33425	+	1.33425i
$183$	−4.89898	−	4.89898i	−0.362143	−	0.362143i
$184$	−2.44949			−0.180579
$185$		0			0
$186$	6.00000	−	12.2474i	0.439941	−	0.898027i
$187$	−24.4949	+	24.4949i	−1.79124	+	1.79124i
$188$	−7.34847	−	7.34847i	−0.535942	−	0.535942i
$189$	19.5959			1.42539
$190$		0			0
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$	−1.00000	−	1.00000i	−0.0721688	−	0.0721688i
$193$	−9.79796	−	9.79796i	−0.705273	−	0.705273i	0.260265	−	0.965537i	$-0.416190\pi$
$193$	−9.79796	−	9.79796i	−0.705273	−	0.705273i	−0.965537	+	0.260265i	$0.916190\pi$
$194$		0			0
$195$		0			0
$196$	−5.00000			−0.357143
$197$	−17.0000	−	17.0000i	−1.21120	−	1.21120i	−0.970632	−	0.240567i	$-0.922666\pi$
$197$	−17.0000	−	17.0000i	−1.21120	−	1.21120i	−0.240567	−	0.970632i	$-0.577334\pi$
$198$	6.00000	−	6.00000i	0.426401	−	0.426401i
$199$	−14.6969			−1.04184			−0.520919	−	0.853606i	$-0.674411\pi$
$199$	−14.6969			−1.04184			−0.520919	+	0.853606i	$0.674411\pi$
$200$		0			0
$201$			4.89898i			0.345547i
$202$	14.6969	−	14.6969i	1.03407	−	1.03407i
$203$	24.0000	−	24.0000i	1.68447	−	1.68447i
$204$			10.0000i			0.700140i
$205$		0			0
$206$	−6.00000			−0.418040
$207$	1.00000	+	1.00000i	0.0695048	+	0.0695048i
$208$	−15.0000	+	15.0000i	−1.04006	+	1.04006i
$209$	9.79796			0.677739
$210$		0			0
$211$	10.0000			0.688428			0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000			0.688428			0.344214	+	0.938891i	$0.388145\pi$
$212$	−1.00000	−	1.00000i	−0.0686803	−	0.0686803i
$213$	−6.00000	+	6.00000i	−0.411113	+	0.411113i
$214$			18.0000i			1.23045i
$215$		0			0
$216$			9.79796i			0.666667i
$217$	−18.2474	+	6.24745i	−1.23872	+	0.424104i
$218$	−19.5959	−	19.5959i	−1.32720	−	1.32720i
$219$		−	6.00000i		−	0.405442i
$220$		0			0
$221$	−30.0000			−2.01802
$222$	7.34847	−	7.34847i	0.493197	−	0.493197i
$223$	3.00000	−	3.00000i	0.200895	−	0.200895i	−0.599489	−	0.800383i	$-0.704629\pi$
$223$	3.00000	−	3.00000i	0.200895	−	0.200895i	0.800383	+	0.599489i	$0.204629\pi$
$224$		−	18.0000i		−	1.20268i
$225$		0			0
$226$		0			0
$227$	2.44949	−	2.44949i	0.162578	−	0.162578i	−0.621130	−	0.783708i	$-0.713326\pi$
$227$	2.44949	−	2.44949i	0.162578	−	0.162578i	0.783708	+	0.621130i	$0.213326\pi$
$228$	2.00000	−	2.00000i	0.132453	−	0.132453i
$229$	−19.5959			−1.29493			−0.647467	−	0.762093i	$-0.724172\pi$
$229$	−19.5959			−1.29493			−0.647467	+	0.762093i	$0.724172\pi$
$230$		0			0
$231$	24.0000			1.57908
$232$	12.0000	+	12.0000i	0.787839	+	0.787839i
$233$	14.6969	+	14.6969i	0.962828	+	0.962828i	0.999333	−	0.0365050i	$-0.0116225\pi$
$233$	14.6969	+	14.6969i	0.962828	+	0.962828i	−0.0365050	+	0.999333i	$0.511622\pi$
$234$	7.34847			0.480384
$235$		0			0
$236$	−12.0000			−0.781133
$237$	−9.79796	+	9.79796i	−0.636446	+	0.636446i
$238$	30.0000	−	30.0000i	1.94461	−	1.94461i
$239$	−4.89898			−0.316889			−0.158444	−	0.987368i	$-0.550648\pi$
$239$	−4.89898			−0.316889			−0.158444	+	0.987368i	$0.550648\pi$
$240$		0			0
$241$		−	24.4949i		−	1.57786i	−0.614486	−	0.788928i	$-0.710637\pi$
$241$		−	24.4949i		−	1.57786i	0.614486	−	0.788928i	$-0.289363\pi$
$242$	15.9217	−	15.9217i	1.02348	−	1.02348i
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$	4.89898			0.313625
$245$		0			0
$246$			14.6969i			0.937043i
$247$	6.00000	+	6.00000i	0.381771	+	0.381771i
$248$	−3.12372	−	9.12372i	−0.198357	−	0.579357i
$249$		−	14.0000i		−	0.887214i
$250$		0			0
$251$		−	9.79796i		−	0.618442i	−0.950990	−	0.309221i	$-0.899932\pi$
$251$		−	9.79796i		−	0.618442i	0.950990	−	0.309221i	$-0.100068\pi$
$252$	−2.44949	+	2.44949i	−0.154303	+	0.154303i
$253$	4.89898	+	4.89898i	0.307996	+	0.307996i
$254$	−7.34847			−0.461084
$255$		0			0
$256$	19.0000			1.18750
$257$	4.89898	−	4.89898i	0.305590	−	0.305590i	−0.537606	−	0.843196i	$-0.680671\pi$
$257$	4.89898	−	4.89898i	0.305590	−	0.305590i	0.843196	+	0.537606i	$0.180671\pi$
$258$	−7.34847	−	7.34847i	−0.457496	−	0.457496i
$259$	−14.6969			−0.913223
$260$		0			0
$261$		−	9.79796i		−	0.606478i
$262$	7.34847	−	7.34847i	0.453990	−	0.453990i
$263$	−17.0000	+	17.0000i	−1.04826	+	1.04826i	−0.0494903	+	0.998775i	$0.515760\pi$
$263$	−17.0000	+	17.0000i	−1.04826	+	1.04826i	−0.998775	+	0.0494903i	$0.984240\pi$
$264$			12.0000i			0.738549i
$265$		0			0
$266$	−12.0000			−0.735767
$267$	−9.79796	+	9.79796i	−0.599625	+	0.599625i
$268$	−2.44949	−	2.44949i	−0.149626	−	0.149626i
$269$	24.4949			1.49348			0.746740	−	0.665116i	$-0.231618\pi$
$269$	24.4949			1.49348			0.746740	+	0.665116i	$0.231618\pi$
$270$		0			0
$271$			9.79796i			0.595184i	0.954693	+	0.297592i	$0.0961834\pi$
$271$			9.79796i			0.595184i	−0.954693	+	0.297592i	$0.903817\pi$
$272$	25.0000	+	25.0000i	1.51585	+	1.51585i
$273$	14.6969	+	14.6969i	0.889499	+	0.889499i
$274$	12.2474			0.739895
$275$		0			0
$276$	2.00000			0.120386
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	0.791466	−	0.611213i	$-0.209318\pi$
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	−0.611213	+	0.791466i	$0.709318\pi$
$278$	−18.0000	+	18.0000i	−1.07957	+	1.07957i
$279$	−2.44949	+	5.00000i	−0.146647	+	0.299342i
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$	−18.0000	−	18.0000i	−1.07188	−	1.07188i
$283$	2.44949	+	2.44949i	0.145607	+	0.145607i	0.776152	−	0.630545i	$-0.217169\pi$
$283$	2.44949	+	2.44949i	0.145607	+	0.145607i	−0.630545	+	0.776152i	$0.717169\pi$
$284$		−	6.00000i		−	0.356034i
$285$		0			0
$286$	36.0000			2.12872
$287$	14.6969	−	14.6969i	0.867533	−	0.867533i
$288$	−3.67423	−	3.67423i	−0.216506	−	0.216506i
$289$			33.0000i			1.94118i
$290$		0			0
$291$		0			0
$292$	3.00000	+	3.00000i	0.175562	+	0.175562i
$293$	4.89898	+	4.89898i	0.286201	+	0.286201i	0.835576	−	0.549375i	$-0.185134\pi$
$293$	4.89898	+	4.89898i	0.286201	+	0.286201i	−0.549375	+	0.835576i	$0.685134\pi$
$294$	−12.2474			−0.714286
$295$		0			0
$296$		−	7.34847i		−	0.427121i
$297$	19.5959	−	19.5959i	1.13707	−	1.13707i
$298$	7.34847	+	7.34847i	0.425685	+	0.425685i
$299$			6.00000i			0.346989i
$300$		0			0
$301$			14.6969i			0.847117i
$302$	−18.0000	−	18.0000i	−1.03578	−	1.03578i
$303$	12.0000	−	12.0000i	0.689382	−	0.689382i
$304$		−	10.0000i		−	0.573539i
$305$		0			0
$306$		−	12.2474i		−	0.700140i
$307$	−12.2474	+	12.2474i	−0.698999	+	0.698999i	−0.964195	−	0.265196i	$-0.914563\pi$
$307$	−12.2474	+	12.2474i	−0.698999	+	0.698999i	0.265196	+	0.964195i	$0.414563\pi$
$308$	−12.0000	+	12.0000i	−0.683763	+	0.683763i
$309$	−4.89898			−0.278693
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	−7.34847	+	7.34847i	−0.416025	+	0.416025i
$313$	15.0000	−	15.0000i	0.847850	−	0.847850i	−0.142014	−	0.989865i	$-0.545358\pi$
$313$	15.0000	−	15.0000i	0.847850	−	0.847850i	0.989865	+	0.142014i	$0.0453579\pi$
$314$		−	24.0000i		−	1.35440i
$315$		0			0
$316$		−	9.79796i		−	0.551178i
$317$	−24.4949	+	24.4949i	−1.37577	+	1.37577i	−0.524136	+	0.851635i	$0.675612\pi$
$317$	−24.4949	+	24.4949i	−1.37577	+	1.37577i	−0.851635	+	0.524136i	$0.824388\pi$
$318$	−2.44949	−	2.44949i	−0.137361	−	0.137361i
$319$		−	48.0000i		−	2.68748i
$320$		0			0
$321$			14.6969i			0.820303i
$322$	−6.00000	−	6.00000i	−0.334367	−	0.334367i
$323$	10.0000	−	10.0000i	0.556415	−	0.556415i
$324$		−	5.00000i		−	0.277778i
$325$		0			0
$326$	−30.0000			−1.66155
$327$	−16.0000	−	16.0000i	−0.884802	−	0.884802i
$328$	7.34847	+	7.34847i	0.405751	+	0.405751i
$329$			36.0000i			1.98474i
$330$		0			0
$331$		−	29.3939i		−	1.61563i	−0.589434	−	0.807817i	$-0.700649\pi$
$331$		−	29.3939i		−	1.61563i	0.589434	−	0.807817i	$-0.299351\pi$
$332$	7.00000	+	7.00000i	0.384175	+	0.384175i
$333$	−3.00000	+	3.00000i	−0.164399	+	0.164399i
$334$	−17.1464			−0.938211
$335$		0			0
$336$		−	24.4949i		−	1.33631i
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	0.908388	−	0.418127i	$-0.137313\pi$
$337$	9.00000	+	9.00000i	0.490261	+	0.490261i	−0.418127	+	0.908388i	$0.637313\pi$
$338$	6.12372	+	6.12372i	0.333087	+	0.333087i
$339$		0			0
$340$		0			0
$341$	−12.0000	+	24.4949i	−0.649836	+	1.32647i
$342$	−2.44949	+	2.44949i	−0.132453	+	0.132453i
$343$	−4.89898	−	4.89898i	−0.264520	−	0.264520i
$344$	−7.34847			−0.396203
$345$		0			0
$346$	12.0000			0.645124
$347$	−5.00000	−	5.00000i	−0.268414	−	0.268414i	0.560047	−	0.828461i	$-0.310783\pi$
$347$	−5.00000	−	5.00000i	−0.268414	−	0.268414i	−0.828461	+	0.560047i	$0.810783\pi$
$348$	−9.79796	−	9.79796i	−0.525226	−	0.525226i
$349$		−	10.0000i		−	0.535288i	−0.963518	−	0.267644i	$-0.913755\pi$
$349$		−	10.0000i		−	0.535288i	0.963518	−	0.267644i	$-0.0862451\pi$
$350$		0			0
$351$	24.0000			1.28103
$352$	−18.0000	−	18.0000i	−0.959403	−	0.959403i
$353$	−11.0000	+	11.0000i	−0.585471	+	0.585471i	−0.936401	−	0.350931i	$-0.885865\pi$
$353$	−11.0000	+	11.0000i	−0.585471	+	0.585471i	0.350931	+	0.936401i	$0.385865\pi$
$354$	−29.3939			−1.56227
$355$		0			0
$356$		−	9.79796i		−	0.519291i
$357$	24.4949	−	24.4949i	1.29641	−	1.29641i
$358$		0			0
$359$		−	6.00000i		−	0.316668i	−0.987386	−	0.158334i	$-0.949388\pi$
$359$		−	6.00000i		−	0.316668i	0.987386	−	0.158334i	$-0.0506123\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	−12.0000	−	12.0000i	−0.630706	−	0.630706i
$363$	13.0000	−	13.0000i	0.682323	−	0.682323i
$364$	−14.6969			−0.770329
$365$		0			0
$366$	12.0000			0.627250
$367$	15.0000	+	15.0000i	0.782994	+	0.782994i	0.980335	−	0.197341i	$-0.0632307\pi$
$367$	15.0000	+	15.0000i	0.782994	+	0.782994i	−0.197341	+	0.980335i	$0.563231\pi$
$368$	5.00000	−	5.00000i	0.260643	−	0.260643i
$369$		−	6.00000i		−	0.312348i
$370$		0			0
$371$			4.89898i			0.254342i
$372$	2.55051	+	7.44949i	0.132238	+	0.386238i
$373$	14.6969	+	14.6969i	0.760979	+	0.760979i	0.976499	−	0.215521i	$-0.0691449\pi$
$373$	14.6969	+	14.6969i	0.760979	+	0.760979i	−0.215521	+	0.976499i	$0.569145\pi$
$374$		−	60.0000i		−	3.10253i
$375$		0			0
$376$	−18.0000			−0.928279
$377$	29.3939	−	29.3939i	1.51386	−	1.51386i
$378$	−24.0000	+	24.0000i	−1.23443	+	1.23443i
$379$		−	20.0000i		−	1.02733i	−0.857991	−	0.513665i	$-0.828287\pi$
$379$		−	20.0000i		−	1.02733i	0.857991	−	0.513665i	$-0.171713\pi$
$380$		0			0
$381$	−6.00000			−0.307389
$382$	29.3939	−	29.3939i	1.50392	−	1.50392i
$383$	−19.0000	+	19.0000i	−0.970855	+	0.970855i	−0.999587	−	0.0287325i	$-0.990853\pi$
$383$	−19.0000	+	19.0000i	−0.970855	+	0.970855i	0.0287325	+	0.999587i	$0.490853\pi$
$384$	17.1464			0.875000
$385$		0			0
$386$	24.0000			1.22157
$387$	3.00000	+	3.00000i	0.152499	+	0.152499i
$388$		0			0
$389$	−4.89898			−0.248388			−0.124194	−	0.992258i	$-0.539635\pi$
$389$	−4.89898			−0.248388			−0.124194	+	0.992258i	$0.539635\pi$
$390$		0			0
$391$	10.0000			0.505722
$392$	−6.12372	+	6.12372i	−0.309295	+	0.309295i
$393$	6.00000	−	6.00000i	0.302660	−	0.302660i
$394$	41.6413			2.09786
$395$		0			0
$396$			4.89898i			0.246183i
$397$	19.5959	−	19.5959i	0.983491	−	0.983491i	−0.0163750	−	0.999866i	$-0.505213\pi$
$397$	19.5959	−	19.5959i	0.983491	−	0.983491i	0.999866	+	0.0163750i	$0.00521255\pi$
$398$	18.0000	−	18.0000i	0.902258	−	0.902258i
$399$	−9.79796			−0.490511
$400$		0			0
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$	−6.00000	−	6.00000i	−0.299253	−	0.299253i
$403$	−22.3485	+	7.65153i	−1.11326	+	0.381150i
$404$			12.0000i			0.597022i
$405$		0			0
$406$			58.7878i			2.91759i
$407$	−14.6969	+	14.6969i	−0.728500	+	0.728500i
$408$	12.2474	+	12.2474i	0.606339	+	0.606339i
$409$	4.89898			0.242239			0.121119	−	0.992638i	$-0.461352\pi$
$409$	4.89898			0.242239			0.121119	+	0.992638i	$0.461352\pi$
$410$		0			0
$411$	10.0000			0.493264
$412$	2.44949	−	2.44949i	0.120678	−	0.120678i
$413$	29.3939	+	29.3939i	1.44638	+	1.44638i
$414$	−2.44949			−0.120386
$415$		0			0
$416$		−	22.0454i		−	1.08087i
$417$	−14.6969	+	14.6969i	−0.719712	+	0.719712i
$418$	−12.0000	+	12.0000i	−0.586939	+	0.586939i
$419$			12.0000i			0.586238i	0.956076	+	0.293119i	$0.0946933\pi$
$419$			12.0000i			0.586238i	−0.956076	+	0.293119i	$0.905307\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−12.2474	+	12.2474i	−0.596196	+	0.596196i
$423$	7.34847	+	7.34847i	0.357295	+	0.357295i
$424$	−2.44949			−0.118958
$425$		0			0
$426$		−	14.6969i		−	0.712069i
$427$	−12.0000	−	12.0000i	−0.580721	−	0.580721i
$428$	−7.34847	−	7.34847i	−0.355202	−	0.355202i
$429$	29.3939			1.41915
$430$		0			0
$431$	6.00000			0.289010			0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000			0.289010			0.144505	+	0.989504i	$0.453841\pi$
$432$	−20.0000	−	20.0000i	−0.962250	−	0.962250i
$433$	15.0000	−	15.0000i	0.720854	−	0.720854i	−0.247925	−	0.968779i	$-0.579749\pi$
$433$	15.0000	−	15.0000i	0.720854	−	0.720854i	0.968779	+	0.247925i	$0.0797487\pi$
$434$	14.6969	−	30.0000i	0.705476	−	1.44005i
$435$		0			0
$436$	16.0000			0.766261
$437$	−2.00000	−	2.00000i	−0.0956730	−	0.0956730i
$438$	7.34847	+	7.34847i	0.351123	+	0.351123i
$439$		−	8.00000i		−	0.381819i	−0.981608	−	0.190910i	$-0.938856\pi$
$439$		−	8.00000i		−	0.381819i	0.981608	−	0.190910i	$-0.0611437\pi$
$440$		0			0
$441$	5.00000			0.238095
$442$	36.7423	−	36.7423i	1.74766	−	1.74766i
$443$	12.2474	+	12.2474i	0.581894	+	0.581894i	0.935423	−	0.353530i	$-0.115019\pi$
$443$	12.2474	+	12.2474i	0.581894	+	0.581894i	−0.353530	+	0.935423i	$0.615019\pi$
$444$			6.00000i			0.284747i
$445$		0			0
$446$			7.34847i			0.347960i
$447$	6.00000	+	6.00000i	0.283790	+	0.283790i
$448$	−2.44949	−	2.44949i	−0.115728	−	0.115728i
$449$	−34.2929			−1.61838			−0.809190	−	0.587547i	$-0.800094\pi$
$449$	−34.2929			−1.61838			−0.809190	+	0.587547i	$0.800094\pi$
$450$		0			0
$451$		−	29.3939i		−	1.38410i
$452$		0			0
$453$	−14.6969	−	14.6969i	−0.690522	−	0.690522i
$454$			6.00000i			0.281594i
$455$		0			0
$456$		−	4.89898i		−	0.229416i
$457$	−21.0000	−	21.0000i	−0.982339	−	0.982339i	0.0175082	−	0.999847i	$-0.494427\pi$
$457$	−21.0000	−	21.0000i	−0.982339	−	0.982339i	−0.999847	+	0.0175082i	$0.994427\pi$
$458$	24.0000	−	24.0000i	1.12145	−	1.12145i
$459$		−	40.0000i		−	1.86704i
$460$		0			0
$461$		−	19.5959i		−	0.912673i	−0.889807	−	0.456336i	$-0.849161\pi$
$461$		−	19.5959i		−	0.912673i	0.889807	−	0.456336i	$-0.150839\pi$
$462$	−29.3939	+	29.3939i	−1.36753	+	1.36753i
$463$	−21.0000	+	21.0000i	−0.975953	+	0.975953i	−0.999718	−	0.0237648i	$-0.992435\pi$
$463$	−21.0000	+	21.0000i	−0.975953	+	0.975953i	0.0237648	+	0.999718i	$0.492435\pi$
$464$	−48.9898			−2.27429
$465$		0			0
$466$	−36.0000			−1.66767
$467$	12.2474	−	12.2474i	0.566744	−	0.566744i	−0.364471	−	0.931215i	$-0.618750\pi$
$467$	12.2474	−	12.2474i	0.566744	−	0.566744i	0.931215	+	0.364471i	$0.118750\pi$
$468$	−3.00000	+	3.00000i	−0.138675	+	0.138675i
$469$			12.0000i			0.554109i
$470$		0			0
$471$		−	19.5959i		−	0.902932i
$472$	−14.6969	+	14.6969i	−0.676481	+	0.676481i
$473$	14.6969	+	14.6969i	0.675766	+	0.675766i
$474$		−	24.0000i		−	1.10236i
$475$		0			0
$476$			24.4949i			1.12272i
$477$	1.00000	+	1.00000i	0.0457869	+	0.0457869i
$478$	6.00000	−	6.00000i	0.274434	−	0.274434i
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$		0			0
$481$	−18.0000			−0.820729
$482$	30.0000	+	30.0000i	1.36646	+	1.36646i
$483$	−4.89898	−	4.89898i	−0.222911	−	0.222911i
$484$			13.0000i			0.590909i
$485$		0			0
$486$			17.1464i			0.777778i
$487$	−15.0000	−	15.0000i	−0.679715	−	0.679715i	0.280221	−	0.959936i	$-0.409592\pi$
$487$	−15.0000	−	15.0000i	−0.679715	−	0.679715i	−0.959936	+	0.280221i	$0.909592\pi$
$488$	6.00000	−	6.00000i	0.271607	−	0.271607i
$489$	−24.4949			−1.10770
$490$		0			0
$491$			19.5959i			0.884351i	0.896928	+	0.442176i	$0.145793\pi$
$491$			19.5959i			0.884351i	−0.896928	+	0.442176i	$0.854207\pi$
$492$	−6.00000	−	6.00000i	−0.270501	−	0.270501i
$493$	−48.9898	−	48.9898i	−2.20639	−	2.20639i
$494$	−14.6969			−0.661247
$495$		0			0
$496$	25.0000	+	12.2474i	1.12253	+	0.549927i
$497$	−14.6969	+	14.6969i	−0.659248	+	0.659248i
$498$	17.1464	+	17.1464i	0.768350	+	0.768350i
$499$	−19.5959			−0.877234			−0.438617	−	0.898674i	$-0.644531\pi$
$499$	−19.5959			−0.877234			−0.438617	+	0.898674i	$0.644531\pi$
$500$		0			0
$501$	−14.0000			−0.625474
$502$	12.0000	+	12.0000i	0.535586	+	0.535586i
$503$	−2.44949	−	2.44949i	−0.109217	−	0.109217i	0.650386	−	0.759604i	$-0.274607\pi$
$503$	−2.44949	−	2.44949i	−0.109217	−	0.109217i	−0.759604	+	0.650386i	$0.774607\pi$
$504$			6.00000i			0.267261i
$505$		0			0
$506$	−12.0000			−0.533465
$507$	5.00000	+	5.00000i	0.222058	+	0.222058i
$508$	3.00000	−	3.00000i	0.133103	−	0.133103i
$509$	19.5959			0.868574			0.434287	−	0.900775i	$-0.357000\pi$
$509$	19.5959			0.868574			0.434287	+	0.900775i	$0.357000\pi$
$510$		0			0
$511$		−	14.6969i		−	0.650154i
$512$	−6.12372	+	6.12372i	−0.270633	+	0.270633i
$513$	−8.00000	+	8.00000i	−0.353209	+	0.353209i
$514$			12.0000i			0.529297i
$515$		0			0
$516$	6.00000			0.264135
$517$	36.0000	+	36.0000i	1.58328	+	1.58328i
$518$	18.0000	−	18.0000i	0.790875	−	0.790875i
$519$	9.79796			0.430083
$520$		0			0
$521$	24.0000			1.05146			0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000			1.05146			0.525730	+	0.850652i	$0.323792\pi$
$522$	12.0000	+	12.0000i	0.525226	+	0.525226i
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	−0.482405	−	0.875948i	$-0.660237\pi$
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	0.875948	+	0.482405i	$0.160237\pi$
$524$			6.00000i			0.262111i
$525$		0			0
$526$		−	41.6413i		−	1.81565i
$527$	12.7526	+	37.2474i	0.555510	+	1.62252i
$528$	−24.4949	−	24.4949i	−1.06600	−	1.06600i
$529$			21.0000i			0.913043i
$530$		0			0
$531$	12.0000			0.520756
$532$	4.89898	−	4.89898i	0.212398	−	0.212398i
$533$	18.0000	−	18.0000i	0.779667	−	0.779667i
$534$		−	24.0000i		−	1.03858i
$535$		0			0
$536$	−6.00000			−0.259161
$537$		0			0
$538$	−30.0000	+	30.0000i	−1.29339	+	1.29339i
$539$	24.4949			1.05507
$540$		0			0
$541$	44.0000			1.89171			0.945854	−	0.324593i	$-0.105227\pi$
$541$	44.0000			1.89171			0.945854	+	0.324593i	$0.105227\pi$
$542$	−12.0000	−	12.0000i	−0.515444	−	0.515444i
$543$	−9.79796	−	9.79796i	−0.420471	−	0.420471i
$544$	−36.7423			−1.57532
$545$		0			0
$546$	−36.0000			−1.54066
$547$	−22.0454	+	22.0454i	−0.942594	+	0.942594i	−0.998439	−	0.0558458i	$-0.982214\pi$
$547$	−22.0454	+	22.0454i	−0.942594	+	0.942594i	0.0558458	+	0.998439i	$0.482214\pi$
$548$	−5.00000	+	5.00000i	−0.213589	+	0.213589i
$549$	−4.89898			−0.209083
$550$		0			0
$551$			19.5959i			0.834814i
$552$	2.44949	−	2.44949i	0.104257	−	0.104257i
$553$	−24.0000	+	24.0000i	−1.02058	+	1.02058i
$554$	−7.34847			−0.312207
$555$		0			0
$556$		−	14.6969i		−	0.623289i
$557$	11.0000	+	11.0000i	0.466085	+	0.466085i	0.900644	−	0.434559i	$-0.143096\pi$
$557$	11.0000	+	11.0000i	0.466085	+	0.466085i	−0.434559	+	0.900644i	$0.643096\pi$
$558$	−3.12372	−	9.12372i	−0.132238	−	0.386238i
$559$			18.0000i			0.761319i
$560$		0			0
$561$		−	48.9898i		−	2.06835i
$562$	−14.6969	+	14.6969i	−0.619953	+	0.619953i
$563$	7.34847	+	7.34847i	0.309701	+	0.309701i	0.844794	−	0.535092i	$-0.179723\pi$
$563$	7.34847	+	7.34847i	0.309701	+	0.309701i	−0.535092	+	0.844794i	$0.679723\pi$
$564$	14.6969			0.618853
$565$		0			0
$566$	−6.00000			−0.252199
$567$	−12.2474	+	12.2474i	−0.514344	+	0.514344i
$568$	−7.34847	−	7.34847i	−0.308335	−	0.308335i
$569$	24.4949			1.02688			0.513440	−	0.858126i	$-0.328371\pi$
$569$	24.4949			1.02688			0.513440	+	0.858126i	$0.328371\pi$
$570$		0			0
$571$			9.79796i			0.410032i	0.978759	+	0.205016i	$0.0657246\pi$
$571$			9.79796i			0.410032i	−0.978759	+	0.205016i	$0.934275\pi$
$572$	−14.6969	+	14.6969i	−0.614510	+	0.614510i
$573$	24.0000	−	24.0000i	1.00261	−	1.00261i
$574$			36.0000i			1.50261i
$575$		0			0
$576$	−1.00000			−0.0416667
$577$	−4.89898	+	4.89898i	−0.203947	+	0.203947i	−0.801689	−	0.597742i	$-0.796065\pi$
$577$	−4.89898	+	4.89898i	−0.203947	+	0.203947i	0.597742	+	0.801689i	$0.296065\pi$
$578$	−40.4166	−	40.4166i	−1.68111	−	1.68111i
$579$	19.5959			0.814379
$580$		0			0
$581$		−	34.2929i		−	1.42271i
$582$		0			0
$583$	4.89898	+	4.89898i	0.202895	+	0.202895i
$584$	7.34847			0.304082
$585$		0			0
$586$	−12.0000			−0.495715
$587$	11.0000	+	11.0000i	0.454019	+	0.454019i	0.896686	−	0.442667i	$-0.145968\pi$
$587$	11.0000	+	11.0000i	0.454019	+	0.454019i	−0.442667	+	0.896686i	$0.645968\pi$
$588$	5.00000	−	5.00000i	0.206197	−	0.206197i
$589$	4.89898	−	10.0000i	0.201859	−	0.412043i
$590$		0			0
$591$	34.0000			1.39857
$592$	15.0000	+	15.0000i	0.616496	+	0.616496i
$593$	−24.4949	−	24.4949i	−1.00588	−	1.00588i	−0.999983	−	0.00590230i	$-0.998121\pi$
$593$	−24.4949	−	24.4949i	−1.00588	−	1.00588i	−0.00590230	−	0.999983i	$-0.501879\pi$
$594$			48.0000i			1.96946i
$595$		0			0
$596$	−6.00000			−0.245770
$597$	14.6969	−	14.6969i	0.601506	−	0.601506i
$598$	−7.34847	−	7.34847i	−0.300501	−	0.300501i
$599$			18.0000i			0.735460i	0.929933	+	0.367730i	$0.119865\pi$
$599$			18.0000i			0.735460i	−0.929933	+	0.367730i	$0.880135\pi$
$600$		0			0
$601$			34.2929i			1.39883i	0.714713	+	0.699417i	$0.246557\pi$
$601$			34.2929i			1.39883i	−0.714713	+	0.699417i	$0.753443\pi$
$602$	−18.0000	−	18.0000i	−0.733625	−	0.733625i
$603$	2.44949	+	2.44949i	0.0997509	+	0.0997509i
$604$	14.6969			0.598010
$605$		0			0
$606$			29.3939i			1.19404i
$607$	22.0454	−	22.0454i	0.894795	−	0.894795i	−0.100174	−	0.994970i	$-0.531940\pi$
$607$	22.0454	−	22.0454i	0.894795	−	0.894795i	0.994970	+	0.100174i	$0.0319401\pi$
$608$	7.34847	+	7.34847i	0.298020	+	0.298020i
$609$			48.0000i			1.94506i
$610$		0			0
$611$			44.0908i			1.78372i
$612$	5.00000	+	5.00000i	0.202113	+	0.202113i
$613$	3.00000	−	3.00000i	0.121169	−	0.121169i	−0.643922	−	0.765091i	$-0.722694\pi$
$613$	3.00000	−	3.00000i	0.121169	−	0.121169i	0.765091	+	0.643922i	$0.222694\pi$
$614$		−	30.0000i		−	1.21070i
$615$		0			0
$616$			29.3939i			1.18431i
$617$	−24.4949	+	24.4949i	−0.986127	+	0.986127i	−0.999905	−	0.0137776i	$-0.995614\pi$
$617$	−24.4949	+	24.4949i	−0.986127	+	0.986127i	0.0137776	+	0.999905i	$0.495614\pi$
$618$	6.00000	−	6.00000i	0.241355	−	0.241355i
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$	−8.00000			−0.321029
$622$		0			0
$623$	−24.0000	+	24.0000i	−0.961540	+	0.961540i
$624$		−	30.0000i		−	1.20096i
$625$		0			0
$626$			36.7423i			1.46852i
$627$	−9.79796	+	9.79796i	−0.391293	+	0.391293i
$628$	9.79796	+	9.79796i	0.390981	+	0.390981i
$629$			30.0000i			1.19618i
$630$		0			0
$631$		−	39.1918i		−	1.56020i	−0.625653	−	0.780101i	$-0.715168\pi$
$631$		−	39.1918i		−	1.56020i	0.625653	−	0.780101i	$-0.284832\pi$
$632$	−12.0000	−	12.0000i	−0.477334	−	0.477334i
$633$	−10.0000	+	10.0000i	−0.397464	+	0.397464i
$634$		−	60.0000i		−	2.38290i
$635$		0			0
$636$	2.00000			0.0793052
$637$	15.0000	+	15.0000i	0.594322	+	0.594322i
$638$	58.7878	+	58.7878i	2.32743	+	2.32743i
$639$			6.00000i			0.237356i
$640$		0			0
$641$			14.6969i			0.580494i	0.956952	+	0.290247i	$0.0937375\pi$
$641$			14.6969i			0.580494i	−0.956952	+	0.290247i	$0.906263\pi$
$642$	−18.0000	−	18.0000i	−0.710403	−	0.710403i
$643$	−27.0000	+	27.0000i	−1.06478	+	1.06478i	−0.0670247	+	0.997751i	$0.521351\pi$
$643$	−27.0000	+	27.0000i	−1.06478	+	1.06478i	−0.997751	+	0.0670247i	$0.978649\pi$
$644$	4.89898			0.193047
$645$		0			0
$646$			24.4949i			0.963739i
$647$	−23.0000	−	23.0000i	−0.904223	−	0.904223i	0.0915749	−	0.995798i	$-0.470810\pi$
$647$	−23.0000	−	23.0000i	−0.904223	−	0.904223i	−0.995798	+	0.0915749i	$0.970810\pi$
$648$	−6.12372	−	6.12372i	−0.240563	−	0.240563i
$649$	58.7878			2.30762
$650$		0			0
$651$	12.0000	−	24.4949i	0.470317	−	0.960031i
$652$	12.2474	−	12.2474i	0.479647	−	0.479647i
$653$	9.79796	+	9.79796i	0.383424	+	0.383424i	0.872334	−	0.488910i	$-0.162605\pi$
$653$	9.79796	+	9.79796i	0.383424	+	0.383424i	−0.488910	+	0.872334i	$0.662605\pi$
$654$	39.1918			1.53252
$655$		0			0
$656$	−30.0000			−1.17130
$657$	−3.00000	−	3.00000i	−0.117041	−	0.117041i
$658$	−44.0908	−	44.0908i	−1.71884	−	1.71884i
$659$		−	30.0000i		−	1.16863i	−0.811525	−	0.584317i	$-0.801362\pi$
$659$		−	30.0000i		−	1.16863i	0.811525	−	0.584317i	$-0.198638\pi$
$660$		0			0
$661$	−40.0000			−1.55582			−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000			−1.55582			−0.777910	+	0.628376i	$0.783720\pi$
$662$	36.0000	+	36.0000i	1.39918	+	1.39918i
$663$	30.0000	−	30.0000i	1.16510	−	1.16510i
$664$	17.1464			0.665410
$665$		0			0
$666$		−	7.34847i		−	0.284747i
$667$	−9.79796	+	9.79796i	−0.379378	+	0.379378i
$668$	7.00000	−	7.00000i	0.270838	−	0.270838i
$669$			6.00000i			0.231973i
$670$		0			0
$671$	−24.0000			−0.926510
$672$	18.0000	+	18.0000i	0.694365	+	0.694365i
$673$	−15.0000	+	15.0000i	−0.578208	+	0.578208i	−0.934409	−	0.356202i	$-0.884072\pi$
$673$	−15.0000	+	15.0000i	−0.578208	+	0.578208i	0.356202	+	0.934409i	$0.384072\pi$
$674$	−22.0454			−0.849157
$675$		0			0
$676$	−5.00000			−0.192308
$677$	−1.00000	−	1.00000i	−0.0384331	−	0.0384331i	0.687629	−	0.726062i	$-0.258652\pi$
$677$	−1.00000	−	1.00000i	−0.0384331	−	0.0384331i	−0.726062	+	0.687629i	$0.758652\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			4.89898i			0.187729i
$682$	−15.3031	−	44.6969i	−0.585985	−	1.71153i
$683$	−2.44949	−	2.44949i	−0.0937271	−	0.0937271i	0.658689	−	0.752416i	$-0.271111\pi$
$683$	−2.44949	−	2.44949i	−0.0937271	−	0.0937271i	−0.752416	+	0.658689i	$0.771111\pi$
$684$		−	2.00000i		−	0.0764719i
$685$		0			0
$686$	12.0000			0.458162
$687$	19.5959	−	19.5959i	0.747631	−	0.747631i
$688$	15.0000	−	15.0000i	0.571870	−	0.571870i
$689$			6.00000i			0.228582i
$690$		0			0
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$	−4.89898	+	4.89898i	−0.186231	+	0.186231i
$693$	12.0000	−	12.0000i	0.455842	−	0.455842i
$694$	12.2474			0.464907
$695$		0			0
$696$	−24.0000			−0.909718
$697$	−30.0000	−	30.0000i	−1.13633	−	1.13633i
$698$	12.2474	+	12.2474i	0.463573	+	0.463573i
$699$	−29.3939			−1.11178
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	−29.3939	+	29.3939i	−1.10940	+	1.10940i
$703$	6.00000	−	6.00000i	0.226294	−	0.226294i
$704$	−4.89898			−0.184637
$705$		0			0
$706$		−	26.9444i		−	1.01407i
$707$	29.3939	−	29.3939i	1.10547	−	1.10547i
$708$	12.0000	−	12.0000i	0.450988	−	0.450988i
$709$	−29.3939			−1.10391			−0.551955	−	0.833874i	$-0.686118\pi$
$709$	−29.3939			−1.10391			−0.551955	+	0.833874i	$0.686118\pi$
$710$		0			0
$711$			9.79796i			0.367452i
$712$	−12.0000	−	12.0000i	−0.449719	−	0.449719i
$713$	7.44949	−	2.55051i	0.278986	−	0.0955174i
$714$			60.0000i			2.24544i
$715$		0			0
$716$		0			0
$717$	4.89898	−	4.89898i	0.182956	−	0.182956i
$718$	7.34847	+	7.34847i	0.274242	+	0.274242i
$719$	4.89898			0.182701			0.0913506	−	0.995819i	$-0.470882\pi$
$719$	4.89898			0.182701			0.0913506	+	0.995819i	$0.470882\pi$
$720$		0			0
$721$	−12.0000			−0.446903
$722$	−18.3712	+	18.3712i	−0.683704	+	0.683704i
$723$	24.4949	+	24.4949i	0.910975	+	0.910975i
$724$	9.79796			0.364138
$725$		0			0
$726$			31.8434i			1.18182i
$727$	17.1464	−	17.1464i	0.635926	−	0.635926i	−0.313622	−	0.949548i	$-0.601542\pi$
$727$	17.1464	−	17.1464i	0.635926	−	0.635926i	0.949548	+	0.313622i	$0.101542\pi$
$728$	−18.0000	+	18.0000i	−0.667124	+	0.667124i
$729$			29.0000i			1.07407i
$730$		0			0
$731$	30.0000			1.10959
$732$	−4.89898	+	4.89898i	−0.181071	+	0.181071i
$733$	−9.79796	−	9.79796i	−0.361896	−	0.361896i	0.502615	−	0.864511i	$-0.332371\pi$
$733$	−9.79796	−	9.79796i	−0.361896	−	0.361896i	−0.864511	+	0.502615i	$0.832371\pi$
$734$	−36.7423			−1.35618
$735$		0			0
$736$			7.34847i			0.270868i
$737$	12.0000	+	12.0000i	0.442026	+	0.442026i
$738$	7.34847	+	7.34847i	0.270501	+	0.270501i
$739$	−24.4949			−0.901059			−0.450530	−	0.892761i	$-0.648765\pi$
$739$	−24.4949			−0.901059			−0.450530	+	0.892761i	$0.648765\pi$
$740$		0			0
$741$	−12.0000			−0.440831
$742$	−6.00000	−	6.00000i	−0.220267	−	0.220267i
$743$	−23.0000	+	23.0000i	−0.843788	+	0.843788i	−0.989349	−	0.145561i	$-0.953501\pi$
$743$	−23.0000	+	23.0000i	−0.843788	+	0.843788i	0.145561	+	0.989349i	$0.453501\pi$
$744$	12.2474	+	6.00000i	0.449013	+	0.219971i
$745$		0			0
$746$	−36.0000			−1.31805
$747$	−7.00000	−	7.00000i	−0.256117	−	0.256117i
$748$	24.4949	+	24.4949i	0.895622	+	0.895622i
$749$			36.0000i			1.31541i
$750$		0			0
$751$	−14.0000			−0.510867			−0.255434	−	0.966827i	$-0.582218\pi$
$751$	−14.0000			−0.510867			−0.255434	+	0.966827i	$0.582218\pi$
$752$	36.7423	−	36.7423i	1.33986	−	1.33986i
$753$	9.79796	+	9.79796i	0.357057	+	0.357057i
$754$			72.0000i			2.62209i
$755$		0			0
$756$		−	19.5959i		−	0.712697i
$757$	9.00000	+	9.00000i	0.327111	+	0.327111i	0.851487	−	0.524376i	$-0.175701\pi$
$757$	9.00000	+	9.00000i	0.327111	+	0.327111i	−0.524376	+	0.851487i	$0.675701\pi$
$758$	24.4949	+	24.4949i	0.889695	+	0.889695i
$759$	−9.79796			−0.355643
$760$		0			0
$761$		−	29.3939i		−	1.06553i	−0.846264	−	0.532764i	$-0.821153\pi$
$761$		−	29.3939i		−	1.06553i	0.846264	−	0.532764i	$-0.178847\pi$
$762$	7.34847	−	7.34847i	0.266207	−	0.266207i
$763$	−39.1918	−	39.1918i	−1.41884	−	1.41884i
$764$			24.0000i			0.868290i
$765$		0			0
$766$		−	46.5403i		−	1.68157i
$767$	36.0000	+	36.0000i	1.29988	+	1.29988i
$768$	−19.0000	+	19.0000i	−0.685603	+	0.685603i
$769$			10.0000i			0.360609i	0.983611	+	0.180305i	$0.0577084\pi$
$769$			10.0000i			0.360609i	−0.983611	+	0.180305i	$0.942292\pi$
$770$		0			0
$771$			9.79796i			0.352865i
$772$	−9.79796	+	9.79796i	−0.352636	+	0.352636i
$773$	1.00000	−	1.00000i	0.0359675	−	0.0359675i	−0.688894	−	0.724862i	$-0.741904\pi$
$773$	1.00000	−	1.00000i	0.0359675	−	0.0359675i	0.724862	+	0.688894i	$0.241904\pi$
$774$	−7.34847			−0.264135
$775$		0			0
$776$		0			0
$777$	14.6969	−	14.6969i	0.527250	−	0.527250i
$778$	6.00000	−	6.00000i	0.215110	−	0.215110i
$779$			12.0000i			0.429945i
$780$		0			0
$781$			29.3939i			1.05180i
$782$	−12.2474	+	12.2474i	−0.437968	+	0.437968i
$783$	39.1918	+	39.1918i	1.40060	+	1.40060i
$784$		−	25.0000i		−	0.892857i
$785$		0			0
$786$			14.6969i			0.524222i
$787$	3.00000	+	3.00000i	0.106938	+	0.106938i	0.758552	−	0.651613i	$-0.225907\pi$
$787$	3.00000	+	3.00000i	0.106938	+	0.106938i	−0.651613	+	0.758552i	$0.725907\pi$
$788$	−17.0000	+	17.0000i	−0.605600	+	0.605600i
$789$		−	34.0000i		−	1.21043i
$790$		0			0
$791$		0			0
$792$	6.00000	+	6.00000i	0.213201	+	0.213201i
$793$	−14.6969	−	14.6969i	−0.521904	−	0.521904i
$794$			48.0000i			1.70346i
$795$		0			0
$796$			14.6969i			0.520919i
$797$	−19.0000	−	19.0000i	−0.673015	−	0.673015i	0.285395	−	0.958410i	$-0.407875\pi$
$797$	−19.0000	−	19.0000i	−0.673015	−	0.673015i	−0.958410	+	0.285395i	$0.907875\pi$
$798$	12.0000	−	12.0000i	0.424795	−	0.424795i
$799$	73.4847			2.59970
$800$		0			0
$801$			9.79796i			0.346194i
$802$		0			0
$803$	−14.6969	−	14.6969i	−0.518644	−	0.518644i
$804$	4.89898			0.172774
$805$		0			0
$806$	18.0000	−	36.7423i	0.634023	−	1.29419i
$807$	−24.4949	+	24.4949i	−0.862261	+	0.862261i
$808$	14.6969	+	14.6969i	0.517036	+	0.517036i
$809$	29.3939			1.03343			0.516717	−	0.856156i	$-0.327154\pi$
$809$	29.3939			1.03343			0.516717	+	0.856156i	$0.327154\pi$
$810$		0			0
$811$	44.0000			1.54505			0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000			1.54505			0.772524	+	0.634985i	$0.218994\pi$
$812$	−24.0000	−	24.0000i	−0.842235	−	0.842235i
$813$	−9.79796	−	9.79796i	−0.343629	−	0.343629i
$814$		−	36.0000i		−	1.26180i
$815$		0			0
$816$	−50.0000			−1.75035
$817$	−6.00000	−	6.00000i	−0.209913	−	0.209913i
$818$	−6.00000	+	6.00000i	−0.209785	+	0.209785i
$819$	14.6969			0.513553
$820$		0			0
$821$			14.6969i			0.512927i	0.966554	+	0.256463i	$0.0825573\pi$
$821$			14.6969i			0.512927i	−0.966554	+	0.256463i	$0.917443\pi$
$822$	−12.2474	+	12.2474i	−0.427179	+	0.427179i
$823$	−27.0000	+	27.0000i	−0.941161	+	0.941161i	−0.998363	−	0.0572018i	$-0.981782\pi$
$823$	−27.0000	+	27.0000i	−0.941161	+	0.941161i	0.0572018	+	0.998363i	$0.481782\pi$
$824$		−	6.00000i		−	0.209020i
$825$		0			0
$826$	−72.0000			−2.50520
$827$	−35.0000	−	35.0000i	−1.21707	−	1.21707i	−0.968654	−	0.248416i	$-0.920090\pi$
$827$	−35.0000	−	35.0000i	−1.21707	−	1.21707i	−0.248416	−	0.968654i	$-0.579910\pi$
$828$	1.00000	−	1.00000i	0.0347524	−	0.0347524i
$829$	−44.0908			−1.53134			−0.765669	−	0.643235i	$-0.777592\pi$
$829$	−44.0908			−1.53134			−0.765669	+	0.643235i	$0.777592\pi$
$830$		0			0
$831$	−6.00000			−0.208138
$832$	−3.00000	−	3.00000i	−0.104006	−	0.104006i
$833$	25.0000	−	25.0000i	0.866199	−	0.866199i
$834$		−	36.0000i		−	1.24658i
$835$		0			0
$836$		−	9.79796i		−	0.338869i
$837$	−10.2020	−	29.7980i	−0.352634	−	1.02997i
$838$	−14.6969	−	14.6969i	−0.507697	−	0.507697i
$839$		−	42.0000i		−	1.45000i	−0.688748	−	0.725001i	$-0.741839\pi$
$839$		−	42.0000i		−	1.45000i	0.688748	−	0.725001i	$-0.258161\pi$
$840$		0			0
$841$	67.0000			2.31034
$842$	12.2474	−	12.2474i	0.422075	−	0.422075i
$843$	−12.0000	+	12.0000i	−0.413302	+	0.413302i
$844$		−	10.0000i		−	0.344214i
$845$		0			0
$846$	−18.0000			−0.618853
$847$	31.8434	−	31.8434i	1.09415	−	1.09415i
$848$	5.00000	−	5.00000i	0.171701	−	0.171701i
$849$	−4.89898			−0.168133
$850$		0			0
$851$	6.00000			0.205677
$852$	6.00000	+	6.00000i	0.205557	+	0.205557i
$853$	9.79796	+	9.79796i	0.335476	+	0.335476i	0.854661	−	0.519186i	$-0.173765\pi$
$853$	9.79796	+	9.79796i	0.335476	+	0.335476i	−0.519186	+	0.854661i	$0.673765\pi$
$854$	29.3939			1.00584
$855$		0			0
$856$	−18.0000			−0.615227
$857$	−24.4949	+	24.4949i	−0.836730	+	0.836730i	−0.988427	−	0.151697i	$-0.951526\pi$
$857$	−24.4949	+	24.4949i	−0.836730	+	0.836730i	0.151697	+	0.988427i	$0.451526\pi$
$858$	−36.0000	+	36.0000i	−1.22902	+	1.22902i
$859$	−39.1918			−1.33721			−0.668604	−	0.743619i	$-0.733108\pi$
$859$	−39.1918			−1.33721			−0.668604	+	0.743619i	$0.733108\pi$
$860$		0			0
$861$			29.3939i			1.00174i
$862$	−7.34847	+	7.34847i	−0.250290	+	0.250290i
$863$	31.0000	−	31.0000i	1.05525	−	1.05525i	0.0568707	−	0.998382i	$-0.481888\pi$
$863$	31.0000	−	31.0000i	1.05525	−	1.05525i	0.998382	−	0.0568707i	$-0.0181123\pi$
$864$	29.3939			1.00000
$865$		0			0
$866$			36.7423i			1.24856i
$867$	−33.0000	−	33.0000i	−1.12074	−	1.12074i
$868$	6.24745	+	18.2474i	0.212052	+	0.619359i
$869$			48.0000i			1.62829i
$870$		0			0
$871$			14.6969i			0.497987i
$872$	19.5959	−	19.5959i	0.663602	−	0.663602i
$873$		0			0
$874$	4.89898			0.165710
$875$		0			0
$876$	−6.00000			−0.202721
$877$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$877$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$878$	9.79796	+	9.79796i	0.330665	+	0.330665i
$879$	−9.79796			−0.330477
$880$		0			0
$881$			4.89898i			0.165051i	0.996589	+	0.0825254i	$0.0262986\pi$
$881$			4.89898i			0.165051i	−0.996589	+	0.0825254i	$0.973701\pi$
$882$	−6.12372	+	6.12372i	−0.206197	+	0.206197i
$883$	9.00000	−	9.00000i	0.302874	−	0.302874i	−0.539263	−	0.842137i	$-0.681297\pi$
$883$	9.00000	−	9.00000i	0.302874	−	0.302874i	0.842137	+	0.539263i	$0.181297\pi$
$884$			30.0000i			1.00901i
$885$		0			0
$886$	−30.0000			−1.00787
$887$	26.9444	−	26.9444i	0.904704	−	0.904704i	−0.0911346	−	0.995839i	$-0.529049\pi$
$887$	26.9444	−	26.9444i	0.904704	−	0.904704i	0.995839	+	0.0911346i	$0.0290494\pi$
$888$	7.34847	+	7.34847i	0.246598	+	0.246598i
$889$	−14.6969			−0.492919
$890$		0			0
$891$			24.4949i			0.820610i
$892$	−3.00000	−	3.00000i	−0.100447	−	0.100447i
$893$	−14.6969	−	14.6969i	−0.491814	−	0.491814i
$894$	−14.6969			−0.491539
$895$		0			0
$896$	42.0000			1.40312
$897$	−6.00000	−	6.00000i	−0.200334	−	0.200334i
$898$	42.0000	−	42.0000i	1.40156	−	1.40156i
$899$	−48.9898	−	24.0000i	−1.63390	−	0.800445i
$900$		0			0
$901$	10.0000			0.333148
$902$	36.0000	+	36.0000i	1.19867	+	1.19867i
$903$	−14.6969	−	14.6969i	−0.489083	−	0.489083i
$904$		0			0
$905$		0			0
$906$	36.0000			1.19602
$907$	31.8434	−	31.8434i	1.05734	−	1.05734i	0.0590889	−	0.998253i	$-0.481180\pi$
$907$	31.8434	−	31.8434i	1.05734	−	1.05734i	0.998253	−	0.0590889i	$-0.0188195\pi$
$908$	−2.44949	−	2.44949i	−0.0812892	−	0.0812892i
$909$		−	12.0000i		−	0.398015i
$910$		0			0
$911$		−	24.4949i		−	0.811552i	−0.913973	−	0.405776i	$-0.867001\pi$
$911$		−	24.4949i		−	0.811552i	0.913973	−	0.405776i	$-0.132999\pi$
$912$	10.0000	+	10.0000i	0.331133	+	0.331133i
$913$	−34.2929	−	34.2929i	−1.13493	−	1.13493i
$914$	51.4393			1.70146
$915$		0			0
$916$			19.5959i			0.647467i
$917$	14.6969	−	14.6969i	0.485336	−	0.485336i
$918$	48.9898	+	48.9898i	1.61690	+	1.61690i
$919$			10.0000i			0.329870i	0.986304	+	0.164935i	$0.0527414\pi$
$919$			10.0000i			0.329870i	−0.986304	+	0.164935i	$0.947259\pi$
$920$		0			0
$921$		−	24.4949i		−	0.807134i
$922$	24.0000	+	24.0000i	0.790398	+	0.790398i
$923$	−18.0000	+	18.0000i	−0.592477	+	0.592477i
$924$		−	24.0000i		−	0.789542i
$925$		0			0
$926$		−	51.4393i		−	1.69040i
$927$	−2.44949	+	2.44949i	−0.0804518	+	0.0804518i
$928$	36.0000	−	36.0000i	1.18176	−	1.18176i
$929$	24.4949			0.803652			0.401826	−	0.915716i	$-0.368376\pi$
$929$	24.4949			0.803652			0.401826	+	0.915716i	$0.368376\pi$
$930$		0			0
$931$	−10.0000			−0.327737
$932$	14.6969	−	14.6969i	0.481414	−	0.481414i
$933$		0			0
$934$			30.0000i			0.981630i
$935$		0			0
$936$			7.34847i			0.240192i
$937$	−19.5959	+	19.5959i	−0.640171	+	0.640171i	−0.950597	−	0.310427i	$-0.899528\pi$
$937$	−19.5959	+	19.5959i	−0.640171	+	0.640171i	0.310427	+	0.950597i	$0.399528\pi$
$938$	−14.6969	−	14.6969i	−0.479872	−	0.479872i
$939$			30.0000i			0.979013i
$940$		0			0
$941$		−	29.3939i		−	0.958213i	−0.877757	−	0.479107i	$-0.840961\pi$
$941$		−	29.3939i		−	0.958213i	0.877757	−	0.479107i	$-0.159039\pi$
$942$	24.0000	+	24.0000i	0.781962	+	0.781962i
$943$	−6.00000	+	6.00000i	−0.195387	+	0.195387i
$944$		−	60.0000i		−	1.95283i
$945$		0			0
$946$	−36.0000			−1.17046
$947$	−31.0000	−	31.0000i	−1.00736	−	1.00736i	−0.999973	−	0.00739197i	$-0.997647\pi$
$947$	−31.0000	−	31.0000i	−1.00736	−	1.00736i	−0.00739197	−	0.999973i	$-0.502353\pi$
$948$	9.79796	+	9.79796i	0.318223	+	0.318223i
$949$		−	18.0000i		−	0.584305i
$950$		0			0
$951$		−	48.9898i		−	1.58860i
$952$	30.0000	+	30.0000i	0.972306	+	0.972306i
$953$	5.00000	−	5.00000i	0.161966	−	0.161966i	−0.621471	−	0.783437i	$-0.713465\pi$
$953$	5.00000	−	5.00000i	0.161966	−	0.161966i	0.783437	+	0.621471i	$0.213465\pi$
$954$	−2.44949			−0.0793052
$955$		0			0
$956$			4.89898i			0.158444i
$957$	48.0000	+	48.0000i	1.55162	+	1.55162i
$958$		0			0
$959$	24.4949			0.790981
$960$		0			0
$961$	19.0000	+	24.4949i	0.612903	+	0.790158i
$962$	22.0454	−	22.0454i	0.710772	−	0.710772i
$963$	7.34847	+	7.34847i	0.236801	+	0.236801i
$964$	−24.4949			−0.788928
$965$		0			0
$966$	12.0000			0.386094
$967$	−3.00000	−	3.00000i	−0.0964735	−	0.0964735i	0.657223	−	0.753696i	$-0.271731\pi$
$967$	−3.00000	−	3.00000i	−0.0964735	−	0.0964735i	−0.753696	+	0.657223i	$0.771731\pi$
$968$	15.9217	+	15.9217i	0.511742	+	0.511742i
$969$			20.0000i			0.642493i
$970$		0			0
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$	−7.00000	−	7.00000i	−0.224525	−	0.224525i
$973$	−36.0000	+	36.0000i	−1.15411	+	1.15411i
$974$	36.7423			1.17730
$975$		0			0
$976$			24.4949i			0.784063i
$977$	14.6969	−	14.6969i	0.470197	−	0.470197i	−0.431782	−	0.901978i	$-0.642115\pi$
$977$	14.6969	−	14.6969i	0.470197	−	0.470197i	0.901978	+	0.431782i	$0.142115\pi$
$978$	30.0000	−	30.0000i	0.959294	−	0.959294i
$979$			48.0000i			1.53409i
$980$		0			0
$981$	−16.0000			−0.510841
$982$	−24.0000	−	24.0000i	−0.765871	−	0.765871i
$983$	−7.00000	+	7.00000i	−0.223265	+	0.223265i	−0.809872	−	0.586607i	$-0.800463\pi$
$983$	−7.00000	+	7.00000i	−0.223265	+	0.223265i	0.586607	+	0.809872i	$0.300463\pi$
$984$	−14.6969			−0.468521
$985$		0			0
$986$	120.000			3.82158
$987$	−36.0000	−	36.0000i	−1.14589	−	1.14589i
$988$	6.00000	−	6.00000i	0.190885	−	0.190885i
$989$		−	6.00000i		−	0.190789i
$990$		0			0
$991$		−	9.79796i		−	0.311242i	−0.987817	−	0.155621i	$-0.950262\pi$
$991$		−	9.79796i		−	0.311242i	0.987817	−	0.155621i	$-0.0497379\pi$
$992$	−27.3712	+	9.37117i	−0.869036	+	0.297535i
$993$	29.3939	+	29.3939i	0.932786	+	0.932786i
$994$		−	36.0000i		−	1.14185i
$995$		0			0
$996$	−14.0000			−0.443607
$997$	9.79796	−	9.79796i	0.310304	−	0.310304i	−0.534723	−	0.845027i	$-0.679584\pi$
$997$	9.79796	−	9.79796i	0.310304	−	0.310304i	0.845027	+	0.534723i	$0.179584\pi$
$998$	24.0000	−	24.0000i	0.759707	−	0.759707i
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.f.a.743.1	yes	4
5.2	odd	4		775.2.f.b.557.1	yes	4
5.3	odd	4	inner	775.2.f.a.557.2	yes	4
5.4	even	2		775.2.f.b.743.2	yes	4
31.30	odd	2		775.2.f.b.743.1	yes	4
155.92	even	4	inner	775.2.f.a.557.1	✓	4
155.123	even	4		775.2.f.b.557.2	yes	4
155.154	odd	2	inner	775.2.f.a.743.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.f.a.557.1	✓	4	155.92	even	4	inner
775.2.f.a.557.2	yes	4	5.3	odd	4	inner
775.2.f.a.743.1	yes	4	1.1	even	1	trivial
775.2.f.a.743.2	yes	4	155.154	odd	2	inner
775.2.f.b.557.1	yes	4	5.2	odd	4
775.2.f.b.557.2	yes	4	155.123	even	4
775.2.f.b.743.1	yes	4	31.30	odd	2
775.2.f.b.743.2	yes	4	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{2} +(-1.00000 + 1.00000i) q^{3} -1.00000i q^{4} -2.44949i q^{6} +(-2.44949 + 2.44949i) q^{7} +(-1.22474 - 1.22474i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 + 1.22474i) q^{2} +(-1.00000 + 1.00000i) q^{3} -1.00000i q^{4} -2.44949i q^{6} +(-2.44949 + 2.44949i) q^{7} +(-1.22474 - 1.22474i) q^{8} +1.00000i q^{9} +4.89898i q^{11} +(1.00000 + 1.00000i) q^{12} +(-3.00000 + 3.00000i) q^{13} -6.00000i q^{14} +5.00000 q^{16} +(5.00000 + 5.00000i) q^{17} +(-1.22474 - 1.22474i) q^{18} -2.00000i q^{19} -4.89898i q^{21} +(-6.00000 - 6.00000i) q^{22} +(1.00000 - 1.00000i) q^{23} +2.44949 q^{24} -7.34847i q^{26} +(-4.00000 - 4.00000i) q^{27} +(2.44949 + 2.44949i) q^{28} -9.79796 q^{29} +(5.00000 + 2.44949i) q^{31} +(-3.67423 + 3.67423i) q^{32} +(-4.89898 - 4.89898i) q^{33} -12.2474 q^{34} +1.00000 q^{36} +(3.00000 + 3.00000i) q^{37} +(2.44949 + 2.44949i) q^{38} -6.00000i q^{39} -6.00000 q^{41} +(6.00000 + 6.00000i) q^{42} +(3.00000 - 3.00000i) q^{43} +4.89898 q^{44} +2.44949i q^{46} +(7.34847 - 7.34847i) q^{47} +(-5.00000 + 5.00000i) q^{48} -5.00000i q^{49} -10.0000 q^{51} +(3.00000 + 3.00000i) q^{52} +(1.00000 - 1.00000i) q^{53} +9.79796 q^{54} +6.00000 q^{56} +(2.00000 + 2.00000i) q^{57} +(12.0000 - 12.0000i) q^{58} -12.0000i q^{59} +4.89898i q^{61} +(-9.12372 + 3.12372i) q^{62} +(-2.44949 - 2.44949i) q^{63} +1.00000i q^{64} +12.0000 q^{66} +(2.44949 - 2.44949i) q^{67} +(5.00000 - 5.00000i) q^{68} +2.00000i q^{69} +6.00000 q^{71} +(1.22474 - 1.22474i) q^{72} +(-3.00000 + 3.00000i) q^{73} -7.34847 q^{74} -2.00000 q^{76} +(-12.0000 - 12.0000i) q^{77} +(7.34847 + 7.34847i) q^{78} +9.79796 q^{79} +5.00000 q^{81} +(7.34847 - 7.34847i) q^{82} +(-7.00000 + 7.00000i) q^{83} -4.89898 q^{84} +7.34847i q^{86} +(9.79796 - 9.79796i) q^{87} +(6.00000 - 6.00000i) q^{88} +9.79796 q^{89} -14.6969i q^{91} +(-1.00000 - 1.00000i) q^{92} +(-7.44949 + 2.55051i) q^{93} +18.0000i q^{94} -7.34847i q^{96} +(6.12372 + 6.12372i) q^{98} -4.89898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3}+O(q^{10}) \) 4 * q - 4 * q^3	\( 4 q - 4 q^{3} + 4 q^{12} - 12 q^{13} + 20 q^{16} + 20 q^{17} - 24 q^{22} + 4 q^{23} - 16 q^{27} + 20 q^{31} + 4 q^{36} + 12 q^{37} - 24 q^{41} + 24 q^{42} + 12 q^{43} - 20 q^{48} - 40 q^{51} + 12 q^{52} + 4 q^{53} + 24 q^{56} + 8 q^{57} + 48 q^{58} - 12 q^{62} + 48 q^{66} + 20 q^{68} + 24 q^{71} - 12 q^{73} - 8 q^{76} - 48 q^{77} + 20 q^{81} - 28 q^{83} + 24 q^{88} - 4 q^{92} - 20 q^{93}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^12 - 12 * q^13 + 20 * q^16 + 20 * q^17 - 24 * q^22 + 4 * q^23 - 16 * q^27 + 20 * q^31 + 4 * q^36 + 12 * q^37 - 24 * q^41 + 24 * q^42 + 12 * q^43 - 20 * q^48 - 40 * q^51 + 12 * q^52 + 4 * q^53 + 24 * q^56 + 8 * q^57 + 48 * q^58 - 12 * q^62 + 48 * q^66 + 20 * q^68 + 24 * q^71 - 12 * q^73 - 8 * q^76 - 48 * q^77 + 20 * q^81 - 28 * q^83 + 24 * q^88 - 4 * q^92 - 20 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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